1. Field of the Invention
The present invention relates to a method for estimating solar radiation flux density and other solar-correlated meteorological variables at a location, based on measurements of the same variables at other locations within the same geographic region for the same period of time. The description of the method is based on hourly measures of the variables but could be used with measurements representing lesser or greater length daytime periods. The method is similarly described using measurements taken 2 meters above the earth""s surface but could be applied to measurements from other distances above the surface. Modeling or extrapolating variables to locations within the region, for which measurements are not available, is typically done using traditional statistical methods such as least squares regression of linear equations of a chosen order, or by employing the techniques of geostatistics, common to hydrology and geology. The later methods are characterized by providing preferential significance to measurements near the location to be estimated. Application of geostatistics to biometeorological applications has been limited due to poor correlations using common geophysical coordinate systems. The method of this invention improves the application of geostatistical techniques to biometeorological estimations through the application of three steps: (1) decomposition of any measurement into two components, the mean measurement from historical observations for the same period of the year and the normalized departure from the mean for the measurement, (2) decomposition of the measured solar radiation flux density into the product of the calculated extraterrestrial radiation at each location and the clearness index, (3) and, transformation of the coordinate system for measured and estimated mean value locations from (x,y,z), typically latitude, longitude, and elevation or depth, to a computed coordinate system (xxe2x80x2,yxe2x80x2,zxe2x80x2) based on the relative calculated extraterrestrial radiation within the region, and one or two additional regionally-specific axes for analysis and modeling of mean values. For a specific (x,y) location, the extraterrestrial radiation flux density is the same each year, on the same day-of-the-year and hour-of-the-day, i.e. a constant that can be calculated.
The value of this method would, at least, provide important information for the engineering of solar photovoltaic applications, agricultural and landscape irrigation management, regional water use allocations, and, passive space conditioning. A person knowledgeable in the fields of geostatistics and biometeorology should be able to implement this method and achieve results superior to other methods of spatial estimation of solar radiation flux density and other solar-correlated meteorological variables.
2. Description of the Prior Art
The method is illustrated for an example region using the synoptic observations made available by the California Irrigation Management Information System (hereafter CIMIS). This network of more than 180 stations depicted in FIG. 1 of this application are scattered throughout the state and the associated database of measurements have been maintained and quality assured since 1982 by the State of California, Department of Water Resources. Each dot on the map of California county boundaries identified in FIG. 1 represents the location of one CIMIS weather station. Details of the network, station locations, and the instruments at each station are described in Technical Elements of CIMIS, The California Irrigation Management Information System published December, 1998 by State of California, The Resources Agency, Department of Water Resources, Division of Planning and Local Assistance. Although the method is demonstrated for this network within the region identified as California, it could be applied to any region supporting a similar synoptic network of meteorological instruments and a database of historical observations. Similarly but not demonstrated, measurements need not be surface-based. Remotely sensed measurements, such as satellite-based images shown in FIG. 8, could be used in the application of this method. Spatial estimation of a variable is commonly done at grid intersection points on a uniform grid created to cover the entire region. From a high-density grid description, utility software can create a contour map of variable value ranges throughout the region, as in FIG. 2. FIG. 2 was created from a data file representing measurements of solar radiation flux density in Watts per square meter on a flat surface at 2 meters for Nov. 10, 1996 from 12 pm to 1 pm Pacific Standard Time. The traditional technique used was linear regression of a cubic equation to the dataset. The range of measurements varied from 89 to 725 Watts per square meter but this traditional method estimated negative values of solar radiation for some parts of the region. For sizing of photovoltaic applications, yearly average solar radiation flux density for every daylight hour of the year would be required. FIG. 3 represents the same traditional technique used in FIG. 1, but applied to the average solar radiation flux density for November 10, 12 pm to 1 pm Pacific Standard Time for all years of record. The appearance of significant areas represented by negative solar radiation would question the application of the technique. A more sophisticated technique would be to consider applying an equation of a higher order or geostatistical techniques to the problem.
Geostatistical analysis is the collection of statistical and other numerical techniques for determining spatial correlations between measured variables within a region, developing models that represent those spatial correlations, and then using those models to estimate variables at other locations within the region. Geostatistics has been widely used in many fields to estimate variables at locations lacking measurement, but most commonly in hydrology and geology.
The first step in a geostatistical analysis would be an attempt to identify spatial correlation structures in the data between pairs of measurements with similar vector separations. Prior to the analysis of correlation however, the number of pairs of samples available for all possible similar separations must be computed and analyzed. FIG. 4 indicates the number of pairs at various intervals of separation available in the database of observations for geostatistical analysis within the region. For a measure of correlation to be calculated for samples with a similar separation, there must be a sufficient number of pairs of samples. Note the value of 549 in the center of the map (FIG. 4). This indicates that there are 549 sample pairs separated by less than xc2xd degree from approximately 150 stations in 18 years of samples for this hour-of-the-year. Consider as an example pair of stations, San Jose located at (xe2x88x92121.95, 37.326) and Sacramento located at (xe2x88x92121.218, 39.65). The vector separation from San Jose to Sacramento would be (0.732, 2.324) which would fall within the interval (1,2). In FIG. 4 at that grid intersection, there are 65 sample pairs with a similar separation. Note also that at (xe2x88x921,xe2x88x922) there are also 65 samples. This sample pair would also be included in those 65 pairs and represents the vector drawn from Sacramento to San Jose, which is equal in magnitude but in the opposite direction of the San Jose to Sacramento vector. Geostatistics accommodates this double counting of sample pairs. As indicated in FIG. 4, it is very important to note that there are only an adequate number of samples for some separations only out to about 3.5 degrees. Hence, further analysis of spatial correlations for these measurements will be limited to separations of 3.5 degrees or less for any direction. Alternatively, this would represent approximately 35% of the maximum separations possible within the region.
The correlation between sample pairs for all possible spacings within the region can be calculated and then reported as a correlogram map as shown in FIG. 5. Computation of the correlogram for all pairs produces the correlogram map (FIG. 5) based on the same average measured values used to create FIG. 3. For those separations with the highest correlation (approximately 0.7), their value would be disregarded due to the fact that they represent only 2 samples as indicated in FIG. 4 at the same coordinates. In the application of geostatistics, it is generally desirable for closely spaced samples to exhibit high correlations and it is expected that correlations would decrease as separations are increased. Analysis of this correlogram map indicates little justification for employing geostatistical techniques.
Pertinent prior art publications in this field are as follows:
1. Allen, R. G., xe2x80x9cAssessing Integrity of Weather Data for Reference Evapotranspiration Estimationxe2x80x9d, Journal of Irrigation and Drainage Engineering, March/April 1996.
2. U.S. Pat. No. 6,343,255, issued Jan. 29, 2002.
3. U.S. Pat. No. 6,345,108, issued Feb. 5, 2002.
The method disclosed and claimed herein is not taught or suggested by the indicated prior art.
3. Definition of Terms Used in this Invention
Clearness Index: A variable used to normalize solar radiation flux density Rs obtained by dividing the mean measured solar radiation Rs by the calculated extraterrestrial radiation flux density Ra. The value of this variable would be expected to be in the range of near zero to less than one. Low values near midday would be due to solar eclipses, extreme dust, heavy smoke, clouds, or rain. However, due to reflection from nearby cumulus clouds, short-interval values slightly exceeding a value of one have been observed.
Example Region: The region chosen as an example is the state of California, USA. The methods reported here might be applied to any greater or lesser region for which a similar network of observations is available. California is a good example for two reasons: the North-to-South extent of the region is significant, and the region represents the boundary between the Pacific Ocean and the continent at latitudes characterized by a mean easterly onshore flow.
Extraterrestrial Radiation Flux Density (Ra): The theoretical solar radiation that would be measured at the top of the atmosphere on a flat surface parallel to the earth surface and along a line from a point on the surface of the earth to the center of the sun. The value could be either the instantaneous flux density or the average for a period such as an hour.
At the earth surface, the solar radiation flux density (Rs) measured by a pyranometer at the same instant would be expected to be less than (Ra) due to atmospheric scattering, reflection, and absorption. However due to reflection from nearby cumulus clouds during generally clear conditions, Rs might exceed Ra for short periods. The average value of extraterrestrial solar radiation flux density Ra for a time interval can be calculated given the location, the day of the year, and, the beginning time and length of the period. Location is usually specified in degrees of latitude North (South is negative) and degrees of longitude East (West is negative).
Geostatistics: A collection of statistical techniques used since the 1950""s for estimation of variables at locations between or beyond measured samples. These techniques are commonly used in geophysical sciences and resource engineering. The methods are applied to a xe2x80x9cfieldxe2x80x9d, and, in this example, the field is the surface of the earth within the state boundaries of California. The fundamental process is to identify and then exploit spatial correlations that are greatest for nearby samples, but then decrease with increased distance between sample locations. These techniques can be used in fields with two or more dimensions, although this example is in 2 dimensions, it could be easily extended to three. Preparing estimates at any location affords greater weight (importance) to samples nearer the estimate location. The distances for improved correlation can be onmi directional (any direction) or directional (preferred directions). Geostatistical methods are commonly used in hydrological models, mining or other resource extraction planning, or pollution management. Although geostatistical methods have been explored in many fields, the method described herein is the first to develop models for solar radiation flux density and correlated variables by using a three-step process: (1) decompose measured variables into mean and departure, (2) decompose solar radiation flux density into the product of extraterrestrial radiation and clearness index, (3) model spatial correlation of mean variable measurements in a transformed coordinate system, (4) model departures of mean values, and then (5) combine mean and departure models.
Hour-of-the-year. The method is employed at the maximum resolution of the example data: hourly averages. At any station location, for a specific day-of-the-year and hour-of-the-day, the extraterrestrial radiation is the same, or constant, every year. Variation in solar radiation flux density at the earth""s surface between yearly samples is only a function of the clearness index for that hour.
Other Solar Correlated Meteorological Variables: Directly intercepted radiation from the sun is the primary energy source for light, warmth, evaporation of liquids, and photochemical reactions (such as photosynthesis) at the earth""s surface. Analysis of historical data revealed significant correlation between solar radiation flux density and other variables: reference evapotranspiration, temperature, and atmospheric moisture parameters.
Reference Evapotranspiration: The United Nations Food and Agriculture Organization (FAO) provides an internationally accepted method for approximating the upward water vapor flux from a carefully defined reference surface of grass. In agricultural production, evapotranspiration represents the water that must be replenished either through precipitation or irrigation. Carefully calculated reference evapotranspiration is multiplied by crop-specific coefficients to estimate the evaporation from surfaces supporting vegetation other than the reference grass surface, such as avocados or alfafa. This permits input to management decisions regarding allocation of water resources among agriculture, wildlife, and other uses.
Solar Radiation Flux Density (Rs): Solar radiation within the visible spectrum falling on a flat surface can be measured by a solar pyranometer such as a LICOR 2000SA used at each CIMIS weather station. The most common units are Watts per square meter. The instruments are calibrated to report the effective radiation flux density normal (perpendicular) to the surface in Watts per square meter averaged for a one hour period. This represents the solar energy available for conversion to useable electricity by photovoltaic materials, for evaporation of water, for the support of photosynthesis by plants, or to controllably increase the internal energy (heat) of a surface or volume.
Synoptic instrument network: The example network used data loggers to repeatedly sample the instrument measurements and then report an average value for a one-hour period defined by an ending time in Pacific Standard Time to a central database. Although the example is for a one-hour period, the method could be applied to other time intervals representing a portion of any daytime period of one hour or less. Application of the method to periods of greater length could be accomplished by summing the results of the aforementioned periods.
Vapor pressure deficit(vpd): A moisture variable commonly used in biometeorology to indicate the xe2x80x9cdrynessxe2x80x9d of the air. When combined with the mean wind speed, it represents the contribution of evapotranspiration due to hot dry winds. Relative humidity is the moisture variable actually measured at the sample locations but any moisture variable can be calculated from relative humidity, temperature, and barometric pressure. Other moisture variables might be dew point temperature, wet bulb temperature, mixing ratio, etc. The barometric pressure of the air is equal to the sum partial pressures of the gases it contains, one of which is water vapor. Water vapor pressure deficit is the difference between the water vapor pressure of a sample of air subtracted from what the water vapor pressure would be if the air were saturated at the same temperature.
This invention is a multivariable statistical method that can be expressed as an algorithm to estimate solar radiation flux density or any solar-correlated variable for any location within a region that includes a synchronous network of weather stations and a database of historical hourly average values of all meteorological variables. Computing estimates for all grid points on a uniform grid covering the region permits contours such as FIG. 19 to be calculated. FIG. 6 is block diagram outlining the method. The solar radiation flux density, Rs, will be used when an example is beneficial. The solar-correlated variables available in this network include air temperature, water vapor pressure, reference evapotranspiration, and wind speed, all provided as hourly averages. The method comprises:
1. Compute data quality and statistics, including mean, maximum, minimum, and variance of all measured variable samples at all locations for this hour-of-the-year over all years available.
2. Analyze spatial correlations all over data history and develop variogram models for both mean and normalized departure variables. Mean variables require a transformation to an alternative coordinate system prior to model development. Measured solar radiation flux density will be normalized to the clearness index.
3. Create a uniform grid mesh over region and estimate the mean and normalized departure variables at all grid intersections utilizing the variogram models developed.
4. Transform mean variable grids back to latitude and longitude.
5. Combine the estimate for the mean and the estimate for the departure from mean at every grid intersection.
6. Draw contours on a map of the region indicating values of the variable over the entire region as shown in FIG. 19.